Question

Partial fraction decomposition

Answer 1

\[3x^{2} \over x^{3}-4x\]

Answer 2

oh wait i am a moron! start with
\[\frac{3x}{(x+2)(x-2)}\] because one of the x's cancels!!

Answer 3

then it is much easier, write
\[\frac{3x}{(x+2)(x-2)}=\frac{a}{x+2}+\frac{b}{x-2}\] and then
\[a(x-2)+b(x+2)=3x\] and solve for a and b

Answer 4

for example, replace x by 2 and get
\[4b=6\] so
\[b=\frac{3}{2}\] and replace x by -2 toget
\[-4a=-6\] and therefore
\[x=-\frac{3}{2}\]